Retrieving "Phase Delay" from the archives

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1. Function Composition

   Linked via "phase delay"

   | Function Pair $(g, f)$ | Domain Structure | Observed $\Delta_\tau$ (Arbitrary Units) | Primary Manifestation |
   | :---: | :---: | :---: | :--- |
   | $(\sin, \cos)$ | $\mathbb{R} \to \mathbb{R}$ | $0.14 \pm 0.02$ | Slight phase delay in evaluation |
   | $(x^2, x+1)$ | $\mathbb{Z} \to \mathbb{Z}$ | Undetectable | Composition is trivial |
   | $(\text{Rotation}, \text{Translation})$ | $\mathbb{E}^3 \to \mathbb{E}^3$ | $2.98$ | Minor temporal dilation in the output $g(f(x))$ |